Data recommended in 2367 that Worf contact Starbase 24 in order to receive a complete record of communications between the Khitomer outpost and the Romulan vessels that attacked the outpost. (TNGepisode: "Redemption")

The apparent contradiction between Gods of Night and A Singular Destiny may indicate that Starbase 24 was able to be restored to at least partial operation shortly after the Borg assault. It is also possible the designation was reassigned to another facility in the interim.